Originally Posted by

**borophyll** Hi all,

I want to prove the following algebraically (that is, NOT with calculus): If an object with initial velocity $\displaystyle v_i$ is accelerated at some constant acceleration over a time $\displaystyle t$, and finishes with a final velocity of $\displaystyle v_f$, then the average velocity of the object is $\displaystyle {v_i + v_f} \over 2$. This average velocity is the equivalent velocity that this object would have to be travelling (without acceleration) to travel the same distance as the object experiencing acceleration as above.

I need to somehow prove this in order to derive the kinematic equations. But how? It is easy to derive the kinematic equations with a knowledge of calculus, but if you are teaching this to someone without a knowledge of calculus, how can this be proven rigorously?